1. Suppose that a perfectly competitive firm's Total Cost function is given by:
TC = 50 + 80q - 10q2 + 0.6q3
a. What is fixed cost equal to? What is Variable Cost equal to?
b. What is Marginal Cost equal to? What is the Average Variable Cost equal to?
c. Find an equation for the inverse supply curve of the firm. Hint: the supply curve presumes profit-maximizing outputs at any market price.
d. Below which market price (a number) will this firm choose to produce 0 output?
e. Choose a market price that is between Average Cost and Average Variable Cost. Will, the firm choose to produce a positive output level?
Depict this output level in a graph that includes all the
appropriate curves. Explain verbally (and with numbers) why this firm would choose to produce the output you chose.
f. What does it mean for a firm to be a price taker? What is the
implication of this for the individual firm's demand curve? You must also mention in your answer the term elasticity (correctly of course).
g. If the firm's cost curve shifted down, what would this do to?
the firm's supply curve? Justify your answer with an example using the short-run total cost curve above.
Q2. Suppose there are two demand curves (e.g two different sets of consumers) for a particular product (two distinct markets that can be segmented-so somehow the consumers in one market cannot buy in the other market and resale from lower-priced consumers to higher-priced consumers is not possible).
The two demand curves are given by the following equations:
Q1 = 14 - P1 (group 1)
Q2 = 12 - 2P2 (group 2)
a. Solve for the inverse demand curve for group 1 and then graph the inverse demand curve with P on the vertical and Q on the horizontal axis.
b. Calculate MR for each group above and graph on the graphs in part a.
c. Suppose MC=AC is constant and equal to 2 for the firm (So the MC curve applies for both groups (because it is the same supplier of a single product for the two groups), although demand and MR are unique to each group since the markets can be segmented. Find the profit-maximizing output, price, and profits in each market. You may assume that TC = AC*Q (cost per unit*number of units). Label the correct price and quantity for each graph in part a.
d. What are the elasticities at the profit-maximizing quantities that you found in part c?
e. Can you say anything about how the price charged in each market relates to the relative price elasticities of demand you calculated in part d? Try to explain intuitively using an example of a real product that you might consume, in which the supplier of a single product can segment the market and in fact charge different prices to two different groups.
f. Now suppose that the above firm cannot segment the two markets. Solve for the single profit-maximizing price and quantity. What are profits equal to?
1. Suppose that a perfectly competitive firm's Total Cost function is given by:
TC = 50 + 80q - 10q2 + 0.6q3
a. What is fixed cost equal to? What is Variable Cost equal to?
b. What is Marginal Cost equal to? What is the Average Variable Cost equal to?
c. Find an equation for the inverse supply curve of the firm. Hint: the supply curve presumes profit-maximizing outputs at any market price.
d. Below which market price (a number) will this firm choose to produce 0 output?
e. Choose a market price that is between Average Cost and Average Variable Cost. Will, the firm choose to produce a positive output level?
Depict this output level in a graph that includes all the
appropriate curves. Explain verbally (and with numbers) why this firm would choose to produce the output you chose.
f. What does it mean for a firm to be a price taker? What is the
implication of this for the individual firm's demand curve? You must also mention in your answer the term elasticity (correctly of course).
g. If the firm's cost curve shifted down, what would this do to?
the firm's supply curve? Justify your answer with an example using the short-run total cost curve above.
Q2. Suppose there are two demand curves (e.g two different sets of consumers) for a particular product (two distinct markets that can be segmented-so somehow the consumers in one market cannot buy in the other market and resale from lower-priced consumers to higher-priced consumers is not possible).
The two demand curves are given by the following equations:
Q1 = 14 - P1 (group 1)
Q2 = 12 - 2P2 (group 2)
a. Solve for the inverse demand curve for group 1 and then graph the inverse demand curve with P on the vertical and Q on the horizontal axis.
b. Calculate MR for each group above and graph on the graphs in part a.
c. Suppose MC=AC is constant and equal to 2 for the firm (So the MC curve applies for both groups (because it is the same supplier of a single product for the two groups), although demand and MR are unique to each group since the markets can be segmented. Find the profit-maximizing output, price, and profits in each market. You may assume that TC = AC*Q (cost per unit*number of units). Label the correct price and quantity for each graph in part a.
d. What are the elasticities at the profit-maximizing quantities that you found in part c?
e. Can you say anything about how the price charged in each market relates to the relative price elasticities of demand you calculated in part d? Try to explain intuitively using an example of a real product that you might consume, in which the supplier of a single product can segment the market and in fact charge different prices to two different groups.
f. Now suppose that the above firm cannot segment the two markets. Solve for the single profit-maximizing price and quantity. What are profits equal to?
