Budget Constraints
Indifference Curves and Utility
Cost Curves
Profit Maximization
Firm Decision Making
100
Given the general Budget Constraint pxx + pyy = I, what is the slope, x-intercept, and y-intercept?
Slope = -px/py ; x-int = I/px ; y-int = I/py
100
What is the Marginal Rate of Substitution (MRS) and what does it tell us about a consumer's preferences?
The MRS = the slope of the indifference curve.
It is the rate at which a consumer is willing to trade one good for another. (i.e. in order for someone to consume one additional unit of good x, they would need to give up a certain number of units of good y). The MRS decreases as you move down (to the right) along the indifference curve.
100
What are the conditions for economies and diseconomies of scale? What do they mean?
Economies of scale: MC < AC; Q is low and AC is decreasing because the falling AFC pulls the AC down and AFC is dominating AVC.
Diseconomies of scale: MC > AC; Q is high and AC is increasing because the rising AVC pulls up the AC and dominates the effect of the falling AFC.
100
What is the profit maximizing condition? What is the profit maximizing condition for a firm in the competitive market model?
Profit Maximizing: MR = MC
Profit Maximizing for a competitive firm: MR = P
100
What is the shut down condition in the Short Run? What is the exit condition in the Long Run?
Shut down condition: TR < VC = P < AVC
Exit condition: TR < TC = P < AC
200
What are the income and substitution effects. How do these effects relate to a Giffen Good?
The income effect: A fall in px boosts the purchasing power of the consumer's income, allowing them to buy more of good x and y.
The substitution effect: A fall in px makes good y more expensive relative to good x, causing the consumer to buy more of good x and less of good y.
For a Giffen Good, the income effect dominates the substitution effect and an in crease in the price of the good raises the quantity demanded, violating the law of demand.
200
In the case of close substitutes and compliments, which of the two goods will have a very bowed indifference curve, and which will have a less bowed curve?
Close substitutes will have a less bowed (flatter) indifference curve (comes from the perfect substitutes case with perfectly straight indifference curves).
Close complements will have more bowed (curved) indifference curves (comes from the perfect complements case with right-angle indifference curves).
200
Which of the following is true about a firm's costs in the long run? (Check all that apply)
a. The cost of some inputs are fixed, while the cost of other inputs are variable
b. The cost of all inputs are variable costs
c. The long-run average variable cost curve is the same as the long-run average total cost curve
d. None of the other options are correct
b. The cost of all inputs are variable costs
c. The long-run average variable cost curve is the same as the long-run average total cost curve
200
What is the Zero-Profit Condition and what does it tell us about price in the Long Run equilibrium for perfectly competitive markets?
At Long Run Equilibrium, the process of firms entering or exiting the market is complete and remaining firms make zero economic profit (i.e. P = MC). The Zero-Profit condition tells us P = MC = AC, but MC = AC at the minimum of the AC curve. Therefore, in the long-run equilibrium, P = minimum AC and firms earn enough profit to cover all costs with nothing remaining.
200
Which of the following is true about a firm's production decision in the short run if the firm thinks at the margin? (Check all that apply)
a. If the market price equals a firm's minimum average variable cost, the firm will be indifferent between shutting down versus not shutting down
b. A firm will only choose to produce the good if the market price is greater than the firm's average total cost
c. It will never be optimal for a firm to produce at a level of output at which its profits are negative
d. A firm will choose to shut down if the market price is lower than the firm's average variable cost
a. If the market price equals a firm's minimum average variable cost, the firm will be indifferent between shutting down versus not shutting down
d. A firm will choose to shut down if the market price is lower than the firm's average variable cost
300
Assume that Destiny has $30 in income, the price of a loaf of bread is $1.50, and the price of a jar of peanut butter is $3. Suppose that at the original income of $30, the price of a loaf of bread increased to $3 and the price of a jar of peanut butter decreased to $2. After the price changes, Destiny can buy a maximum of ______ loaves of bread or a maximum of ______ jars of peanut butter.
A) 10 fewer; 5 more
B) 15 fewer; 10 more
C) 10 fewer; 10 more
D) 15 fewer; 5 more
A) 10 fewer; 5 more
300
Suppose that Fiona’s marginal utility from drinking milk is 5 utils per ounce and her marginal utility from eating cereal is 10 utils per ounce. If the price of milk is 50 cents per ounce and the price of cereal is 80 cents per ounce, is Fiona maximizing her utility? If so, explain how you know. If not, explain how she should change her spending to increase her utility.
The rational spending rule implies that at the optimal consumption bundle: (MUm/Pm)=(MUc/Pc). Thus, since 5/50<10/80, we know that Fiona is not maximizing her utility. She should decrease her consumption of milk and increase her consumption of cereal, putting her money where she gets the biggest bang for her buck.
300
Consider a firm in a perfectly competitive market. Assume that labor is variable in the short run and capital is fixed. In addition, assume that marginal cost decreases initially and then eventually increases.
a. Draw a standard set of short-run cost curves for the firm. Be sure to label both the horizontal and vertical axis. Your graph should include the firm’s marginal cost
curve (MC), average fixed cost curve (AFC), average variable cost curve (AVC) and average total cost curve (ATC).
b. On your graph for part a, label the break-even point and the shut-down point.
c. Suppose the equilibrium price is above the break-even point. Sketch the firm’s profit-maximizing level of output, and shade in the area that represents the firm’s economic profit or loss.
300
In a perfectly competitive market, a firm's total cost curve is given by TC = 2Q2 + 50Q + 600 and it's marginal cost curve is given by MC = 4Q + 50. If the market price is p=350 and the firm maximizes it's profits, how many units of the good will the firm produce?
P = MC: 350 = 4Q + 50; Q = 75
ATC = 2Q + 50 + (600/Q); AVC = 2Q + 50
P>ATC(75) and P>AVC(75), so the firm will produce 75 units.
300
A firm analyzes the effects of raising its current level of output and finds that doing so will cause its average total cost to increase. If the firm pays both fixed and variable costs of production, which of the following must be true? (Check all that apply)
a. The marginal cost curve is less than the average total cost
b. The effect of average variable cost increasing dominates the effect of average fixed cost decreasing
c. The marginal cost is greater than the average total cost
d. The effect of average fixed cost decreasing dominates the effect of average variable cost increasing
b. The effect of average variable cost increasing dominates the effect of average fixed cost decreasing
c. The marginal cost is greater than the average total cost
400
Sketch the budget constraint for jeans and t-shirts under the condition that the price of blue jeans is $50, and the price of t-shirts is $10 for the first 50 t-shirts and then drops to $5 for any additional t-shirt. Assume that income is equal to $1000. Put blue jeans on the y-axis and t-shirts on the x-axis. Label the x-intercept, the y-intercept and the slope of the budget constraint.
BC (first 50 shirts): 10x + 50y = 1000, slope = -1/5;
BC (after 50 shirts): 5x + 50y = 500 {500 is how much income is left after buying 50 shirts}, slope = -1/10;
y-intercept:1000/50 = 20;
x-intercept: 50+ (500/5) = 150; point where slopes change: (50,10)
400
Suppose that Geoff loves beef and hates seafood. In addition, suppose that the marginal utility of beef is decreasing and that the marginal disutility of seafood is increasing.
a. Sketch a few of Geoff’s indifference curves for beef and seafood, putting beef on the x-axis and seafood on the y-axis. Show the direction in which Geoff’s utility is increasing.
b. Suppose that Geoff has $64 dollars to spend on seafood and beef, and suppose that the price of seafood is $10/lb and that the price of beef is $8/lb. Assuming that Geoff maximizes his utility, how many pounds of beef and seafood will Geoff consume?
a.
b. He will consume 8 lbs of beef and no seafood
400
Suppose a firm's total cost curve is given by
TC = (1/8)Q2 + 512
and it's marginal cost curve is given by
MC = (1/4)Q
At what Q does the firm minimize its average total costs?
MC = AVC: (1/4)Q = (1/8)Q + (512/Q)
Q = 64
400
Suppose Scott owns a small company that makes brooms. Assume that the market for brooms is perfectly competitive, and the equilibrium price of a broom is $15. Scott’s total production costs vary depending on the number of brooms he makes
each day, as shown in the table below.
a. When Scott makes 4 brooms per day, what is his average variable cost? Show your work.
b. What is the profit-maximizing number of brooms for Scott to make each day? Carefully explain your answer.
c. What is Scott’s economic profit at his profit-maximizing level of output? Show your work.
a. When Q = 4, TC = $66 and TVC = $66 - $18 = $48, so AVC = $48/4 = $12
b. Scott will continue to produce brooms as long as the marginal cost of an additional broom is less than or equal to the price of a broom. The MC of the 3 rd
broom is $14, which is less than $15, but the MC of the 4 th broom is $18, which is greater than $15. So, Scott will make 3 brooms.
c. When Q=3, Scott’s profit equals $15(3) – $48 = -$3.
400
Suppose Nicholas owns a business making Christmas tree ornaments. Currently, he makes 200 ornaments a month. At this level of production, each additional ornament takes him 30 minutes to make and costs him $10 in materials. Nicholas makes his ornaments in a small art studio that he rents for $400 a month. Nicholas can easily increase or decrease the amount of time he spends making ornaments, and he can
easily go to the store to buy additional materials to make the ornaments, but he has a year-long lease on his studio. Nicholas values his time at $10 per hour. Other than his time, the cost of the materials and the rent on his studio, Nicholas has no additional production costs. His marginal cost of making an additional ornament each month is $15 and the anverage fixed cost of each ornament is $2.
a. Assuming that it’s not in Nicholas’s interest to shut down, should he change his current monthly level of production if he can sell each ornament for $20? If so, explain how his current production should change, and if not, explain why not.
b. How would Nicholas’s profit-maximizing level of output each month differ if his monthly rent were $350 instead of $400? Explain.
c. How would Nicholas’s profit-maximizing level of output each month differ if the materials to make each ornament cost $11 instead of $10? Explain.
a. Since price is greater than marginal cost ($20>$15), Nicholas should increase his
production.
b. If Nicholas’s rent were $350 instead of $400, this would not affect the marginal cost of making an additional ornament each month (since Nicholas’s rent is a fixed cost). Thus, his profit maximizing level of output wouldn’t change.
c. His profit-maximizing level of output would be lower if the cost of the materials used to make each ornament were $11 instead of $10 because the marginal cost of making each ornament would be higher.
500
Suppose Toni has $30 a week to spend on avocados and tomatoes. The price of an avocado is $3, and the price of a tomato is $1.50. Currently, Toni consumes 5 avocados and 10 tomatoes each week. At this consumption bundle, her marginal utility from an additional tomato is 6 utils, and her marginal utility from an additional avocado is 12 utils.
a. Draw Toni’s budget constraint for tomatoes and avocados, putting avocados on the y-axis and tomatoes on the x-axis. Label the x-intercept, the y-intercept and the slope. Be sure to also label your axes.
b. At Toni’s current consumption bundle, is she spending all of her income? Is she maximizing her utility? If so, explain how you know this. If not, how should Toni reallocate her spending between avocados and tomatoes? Briefly explain your answer.
c. At Toni’s current consumption bundle, how many avocados is she willing to give up to get an additional tomato?
a.
b. Yes. 5*$3 + 10*$1.50 = $30. MUa/Pa=(12 utils per additional avocado)/($3 per additional avocado)=4 utils per dollar on avocados and MUt/Pt=(6 utils per additional tomato)/($1.50 per additional tomato)=4 utils per tomato. Since she gets the same bang for her buck on tomatoes and avocados, Toni is maximizing her utility and should not reallocate her spending
c. his is her MRS=MUt/MUa=6/12. She is willing to give up 1/2 of an avocado to get a tomato.
500
Suppose that you have $20 dollars a month to spend on lettuce. The price of iceberg lettuce is $1.00 per head and the price of red leaf lettuce is $2.00 per head (iceberg lettuce and red leaf lettuce are two kinds of lettuce). Assume that your marginal rate of substitution between iceberg lettuce and red leaf lettuce is constant and equal to 1.
a. Sketch your monthly budget constraint for lettuce. Place iceberg lettuce on the x-axis and red leaf lettuce on the y-axis. Be sure to label the x-intercept, the y-intercept and the slope of the budget constraint.
b. On the same graph, sketch a few of your indifference curves between iceberg lettuce and red leaf lettuce. Draw the indifference curves with dashed lines and label their slope.
c. What does the fact that your marginal rate of substitution equals 1 imply about your preferences for these two products?
d. Given your prices, income and preferences, how many heads of iceberg lettuce and red leaf lettuce will you purchase every month.
a. b.
c. It implies that you’re willing to trade off the two goods on a one-to-one basis. That is, you’re willing to give up one head of iceberg lettuce for one head of red leaf lettuce. [Note: the fact that the marginal rate of substitution is also constant implies that the two goods are perfect
substitutes.]
d. You will purchase 20 heads of iceberg lettuce and no heads of red leaflettuce.
500
A firm's average total cost curves is given by ATC = Q + (500/Q) and its marginal cost curve is given by MC = 2Q. If the market price is p=50, what is firm's profit?
Profit = TR - TC; TR = PxQ; TC = ATCxQ; P=MC
P=MC: 50 = 2Q; Q = 25
Profit = (25)(50) - ((25)2+500) = 1250 - 1125 = 125
500
The figure above shows the cost curves of a profit-maximizing firm in a perfectly competitive market. The price of the good in this market equals $7.
a. What is the quantity that maximizes the firm’s profit? Justify.
b. How much is the firm's average total cost, and average variable cost at the profit maximizing quantity?
c. How much is the total cost, variable cost, and fixed costs for this firm at the profit maximizing quantity? Show your calculations.
d. How much is the firm’s total revenue and profit at the profit maximizing quantity? Show the profit as an area in the graph below.
a. The quantity that maximizes the firm’s profit is such that Price (the marginal benefit of producing and selling and extra unit) is equal to the Marginal Cost, as long as Price is above the minimum of the Average Variable costs. Since P = $7, it is above the minimum of the AVC, and thus the quantity that maximizes profit is 40 units per day.
b. At the profit maximizing quantity of 40 units per day, the firm’s average total cost is $4 per unit and the firm’s average variable cost is $3 per unit.
c. Total Cost = ATC * Q = $4 * 40/day = $160 per day.
Variable Cost = AVC * Q = $3 * 40/day = $120 per day. Fixed Cost = Total Cost – Variable Cost = $40 per day.
d. Total Revenue = P * Q = $7 * 40/day = $280 per day.Profit = Total Revenue – Total Cost = $280/day - $160/day = $120 per day. The profit can be represented in the graph above as the area of a rectangle whose height = (P –ATC ) = ($7 - $4) = $3 and the base is the quantity = 40 units per day. The area of the rectangle is $3*40/day = $120 per day, as the graph shows.
500
a. How many units will the firm sell if it decides to charge a price of $10 for each unit? Explain your answer.
b. Label the shutdown point in the graph and briefly explain what the firm will do if the price is below that point and why.
a. Zero. Since the market is perfectly competitive, people have information about all the market, the goods sold are indistinguishable from each other, and there are many sellers. Hence, if this firm decides to increase the price above the market price, buyers
will go and buy from other firms, and not purchase from this firm at all.
b. If the price is below the shutdown point, the firm will not produce any product in the short run, because the price for every unit of product is not enough to cover the variable factors of production needed to produce that unit of product. In other words, below that point, marginal revenue (which is price in perfectly competitive markets) is less than marginal cost. See graph below.
