Suppose that a typical firm in a monopolistically competitive industry faces a demand curve given by:

q = 60 − (1/2)p, where q is quantity sold per week.

The firm’s marginal cost curve is given by: MC = 60.

How much will the firm produce in the short run?

What price will it charge?

To determine the firm's production level and price in the short run, we need to find the profit-maximizing output quantity and corresponding price.

First, we need to find the firm's marginal revenue (MR) curve, as this is needed to determine the profit-maximizing quantity. In a monopolistically competitive market, the demand curve can also be seen as the firm's average revenue (AR) curve.

To find the marginal revenue, we need to take the derivative of the demand curve with respect to quantity (q). The demand curve is given as q = 60 − (1/2)p. To isolate p, we can rearrange the equation as p = 120 - 2q.

Next, we differentiate both sides of the equation with respect to q:
dp/dq = -2

The marginal revenue (MR) curve will be twice the value of the slope of the demand curve.

MR = 2*(-2) = -4

Now that we have the marginal revenue, we can find the output level where MR equals marginal cost (MC) to maximize profit.

In the short run, the firm will produce where MR = MC. The marginal cost (MC) is given as MC = 60.

-4 = 60

Rearranging the equation, we get:
q = 64

So, the firm will produce a quantity of 64 units in the short run.

To determine the price the firm charges, we substitute the quantity (q = 64) into the demand curve:

q = 60 − (1/2)p
64 = 60 - (1/2)p

Rearranging the equation, we can solve for p:
(1/2)p = 60 - 64
(1/2)p = -4
p = -8

Since price cannot be negative in this context, the answer (-8) suggests that there might be an error or the equation is not applicable in this case. Please double-check the given information and equations to ensure accuracy.