How do I calculate the price and quantity being produced in the short run with only the following information?
q = 60 - (1/2)p
MC = 60
See response to previous question.
To calculate the price and quantity being produced in the short run, we need to find the intersection of the market demand curve and the firm's marginal cost curve.
Step 1: Start with the market demand equation.
The given information includes:
q = 60 - (1/2)p
This equation represents the market demand curve. The quantity demanded (q) is a function of the price (p).
Step 2: Set the market demand equal to the firm's quantity.
We know that the quantity being produced by the firm is the same as the quantity demanded in the market in the short run. So, set q equal to the firm's quantity:
q = Q
Step 3: Substitute the firm's quantity into the market demand equation.
Replace q with Q in the market demand equation:
Q = 60 - (1/2)p
Step 4: Find the firm's marginal cost (MC) equation.
The given information also mentions that the firm's marginal cost is 60.
Step 5: Set the firm's marginal cost equal to the market price.
Since the market price (p) is the same as the firm's marginal cost in the short run, we can set p equal to MC:
p = MC = 60
Step 6: Substitute the market price into the market demand equation.
Replace p with 60 in the market demand equation:
Q = 60 - (1/2)(60)
Step 7: Solve for the firm's quantity.
Simplify the equation:
Q = 60 - 30
Q = 30
The quantity being produced by the firm in the short run is 30 units.
Step 8: Substitute the firm's quantity into the market demand equation to find the market price.
Replace Q with 30 in the market demand equation:
30 = 60 - (1/2)p
Step 9: Solve for the market price.
Rearrange the equation to isolate p:
(1/2)p = 60 - 30
(1/2)p = 30
p = 2 * 30
p = 60
The market price in the short run is $60 per unit.
Therefore, in the short run, the firm would produce 30 units at a price of $60 per unit.