# solve the following questions Image transcription text The following production function describes the output of a local Pittsburgh mime troupe’s performances given the labor of

solve the following questions Image transcription text The following production function describes the output of a local Pittsburgh mime troupe’s

performances given the labor of its performers:

q = 217

where q denotes the hours of performances provided and I denotes hours of labor input by

performers. The troupe is a price-taker both for performances (which sell for P) and for performers

(which can be hired at the wage rate of w per hour).

What is the total cost function [C (q)] for the troupe?

b.

Solve for the profit maximizing number of performer hours [(P, w)], i.e., the troupe’s

demand for labor. What is the profit function [x(P, w)] for this troupe? Describe the

homogeneity of the profit function with respect to P and w.

C.

What is the supply function [q(P, w)] for the troupe’s mime performances?

d

Use the envelope theorem (Shephard’s Lemma) and the profit function you found in part (b)

to double check your derivation of the troupe’s demand for labor function [1(P, w)]. Image transcription text Question 2 All ﬁrms in a competitive industry have the following long-run total cost curve:

C(q) = cf’ —2q2 + 4q

where q is the output of the ﬁrm.

3. Compute the long run equilibrium price and explain how you obtain the result.

[20 marks] Image transcription text Consider the following function:

f(x1, X2) = Ax1.5+x2

where x, 2 0, X2 2 0, A 2 0, 0 <b<1.

a) Suppose that the preferences of a consumer regarding the consumption of goods x, and

X2 are represented by function U = f(x1, x2) above. Suppose also that the consumer is

endowed with some disposable income Y > 0 and faces prices p, and p2 respectively for

goods x1 and X2.

i) Derive and describe the demand of the consumer for goods x, and x2. [20 marks]

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