2. Assume that the demand for welding services is D(P) = 34-P/2, and the inverse

Question

2. Assume that the demand for welding services is D(P) = 34-P/2, and the inverse supply function is PS(Q)

= 4 + 10Q + Q2. This supply curve represents the long run supply curve of the incumbent firms already in

the market, but there is free entry into the market.

(a) At what market prices can a new firm enter profitably?

The last three parts refer to a long run that includes the actions of potential entrants.

(b) What is the long run equilibrium price?

(c) Draw the long run supply curve, and calculate the inverse long run supply function.

(d) What is the long run equilibrium quantity?

3. The problem is to choose x to maximize f(x;alpha) = alpha x - 3x^2, where alpha is exogenous, subject to the constraint

x $0.

(a) For this problem, which values of x are on the boundary, and which are in the interior?

(b) Calculate the first-order condition for this problem.

(c) If alpha=12, then which value of x solves the problem? Justify your answer carefully.

(d) If alpha=-2, then which value of x solves the problem? Justify your answer carefully. What is the

maximized value of f?

(e) For which possible values of alpha does this problem have a solution on the boundary?

Explanation / Answer

a.

34-P/2 = Q

68-P =2Q

P= 68-2Q

PS(Q) = 4 + 10Q + Q2

68-2Q=4 + 10Q + Q2

4 + 10Q + Q2-68+2Q =0

Q2-64+12Q= 0

Solve the above equation get the value

Q= -16 and 4

So we take Q= 4

Putting Q=4 in P= 68-2Q

We get P =68-8 = $60

Hence, the new firm at price $60, can enter profitably

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