A firm’s total cost function is TC = 2 q^ 2 + 5 q + 10 . The firm is a price tak

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

Suppose q is the quantity of goods produced and sold

Before subsidy

TC = 2q^2 + 5q+ 10

TR= 25q

Equating TC=TR

q =9 where TC = 2 (9^2)+ 5(9) +10 = 217

TR = 25* 9 = 225

Profit = 225-217 =9 (before subsidy)

After susidy : Cost will be reduced by 25

TC = 2q^2 + 5q+ 10 - 25 (subsidy)

TR= 25q

Equating TC=TR

q=10

TC = 2 (10^2) + 5(10) +10 -25 = 235

TR= 25 *10 = 250

Profit = 250-235 = 15

If the firm produces the same quantity as it was producing before subsidy i.e. 9 units then Profit = profit before subsidy + 25 = 8 + 25 = 33

b) If the firm gets 4$ subsidy for every unit then TC = 2(q^2) + 5q+ 10 - 4q = 2(q^2) + q + 10

Before subsidy

TC = 2q^2 + 5q+ 10

TR= 25q

Equating TC=TR

q =9 where TC = 2 (9^2)+ 5(9) +10 = 217

TR = 25* 9 = 225

Profit = 225-217 =9 (before subsidy)

After susidy

TC = 2(q^2) + q + 10

TR = 25q

Equating TR=TC

q = 11

TC = 2(11^2)+11+10=263

TR= 25(11) = 275

Profit = 275- 263 = 12

If firm produces more than 11 units under option 2, then the total cost will be more than total revenue and the firm will incur loss; so the frim should produce 11 units.

c) firm should choose option 2 as comparing both the options firm will experience more profit by accepting option 2.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.