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Tutorial Questions Week 6

ECON8025

Semester 2, 2022.

Exercise 1. Suppose the expenditure function derived from a consumer’s expenditure minimization problem is given by :

e (p, u) =

Evaluate the EV and CV for this consumer for the change from (p1(∗), 2, m¯)  = (1, 1, 1) to (1, 2, m¯) = (1/2, 1, 1).

Exercise 2. Consider a competitive firm with a cost function defined by c(y) = ay2 + b for y > 0, and c(0) = 0, where a, b > 0. Interpret b as a fixed cost, which has already been incurred in the short run, but can be avoided in the long run.

(i) Compute the output level at which the average cost AC(y) attains a minimum. If b represents a fixed cost, at which output level does the variable cost ay2 attain a minimum?

(ii) Derive the firm’s short-run and long-run supply functions as a function of price p.

(iii) Compute the firm’s (short-run) producer surplus at a price p using the integral of the supply function, and confirm that it equals profits plus the fixed cost b.

(iv) Compute the firm’s long-run producer surplus at a price p, when b is a quasi- fixed/variable cost that can be recovered if production is shut down.

Exercise 3. Farmers produce corn using land and labour. The labour cost to produce q bushels of corn is c(q) = q2 . There are fifty identical farms currently in operation which all behave competitively.

1. What is the individual farmer’s supply curve for corn?

2. What is the market supply curve for corn?

3. Suppose the demand for corn is

x (p) = 200 − 50p

What is the equilibrium price and quantity sold?

4. What rental cost for a farm’s land would make your answer from (c) a long run equilibrium?

5. Suppose now that the rental cost for a farm’s land was 1.  What would be the long-run equilibrium number of farms producing corn?