A firm’s total cost function is TC = 2q 2 + 5q +10 . The firm is a price taker a
ID: 1193240 • Letter: A
Question
A firm’s total cost function is TC = 2q 2 + 5q +10 . The firm is a price taker and the market price for its product is $25. The firm also receives a subsidy from the government because it is operating in a high tech industry and the government encourages such high tech firms. The government has two subsidy options. In option 1, the firm can receive a fixed $25 subsidy. In option 2, the firm receives $4 for each unit of its products.
a. In option 1, how many will it produce to maximize total profit (including the subsidy)? How much is total cost? Profit before subsidy? How much subsidy does it receive? How much is its total profit including subsidy?
b. In option 2, how many will it produce to maximize profit (including the subsidy)? How much is total cost? Profit before subsidy? How much subsidy does it receive? How much is its total profit including subsidy?
c. Which option would the firm choose?
Explanation / Answer
Assumpion: Units cant be produced in decimals so for calculation of units, whole number is considered.
It is suggested to opt for option 2 as profit in this case is more. Please go through th calculations
Before subsidy output produced and sold = 9 units (TR=TC) (2Q^2+5Q+10=25Q)
At this quantity Cost = 217 and Revenue = 25* 9 = 225; so profit = 225-217 = Rs 8
Option 1 Total cost will be reduced by amount of subsidy 2q^2+5q+10-25
Total revenue = 25 q
Equating TR=TC ; q= 10 units
TC= 2(10^2)+5(10)+10-25 = 250-15 = 235
TR = 25*10= 250
Profit = 250-235 = 15
Option 2
Total cost will be reduced by 4q. So new Total cost = 2(q^2)+5q+10-4q = 2(q^2)+q+10
Total revenue = 25q
Equating TR=TC ; q=11 units
Total cost = 2(11^2) + 11 + 10 = 242+21 = 263
Total revenue = 25*11 = 275
Profit = 275-263 = 12
by comparing both the subsidies offered by the government ; Profit will be more under option b will be more profitable i.e. by producing 11 units and getting profit of 12.
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