Question

7 A firm has total cost of TC(y)=y²+1 and marginal cost of MC(y)=2y. What is the firm's producer's surplus at price $8?

Group of answer choices

16

neither one is correct

10

17

15

8 Suppose there are 10 firms in an industry. Each firm has total cost of TC(y)=y²+1 and marginal cost of MC(y)=2y. What is the industry supply at $6?

Group of answer choices

3

neither one is correct

30

12

36

Answer 1

Question 7.

We are given the firm's total cost function as,

TC(y) = y^2 + 1

Here y = units of output produced.

And firm's marginal cost is given as,

MC = 2y.

And we now need to calculate the firm's producer surplus at a price of $8.

To calculate the producer's surplus for this firm we first need to calculate the units of output that this firm will produce at a price of $8. For that we just need to equate price with marginal cost because the firm chooses to produce as long as marginal cost is equal to price.

MC = price

2y = 8

y = 8/2 = 4

So at a price of $8 the firm will produce 4 units. And now let's calculate the producer's surplus.

To calculate the producer's surplus we just need to find the difference between total revenue the firm gets and its total cost.

Producer surplus = total revenue - total cost

Producer surplus = P×y - (y^2+1)

Here y= 4 and P = $8

Putting this into our formula we get,

Producer surplus = 4×8 - (4^2 + 1)

Producer surplus = 32 - (16 +1)

Producer surplus = 32 - 17 = 15

So the firm's producer surplus in this case will of $15.

So correct option for this question is option e, 15.

Question 8.

Now there are 10 firms in the Industry and we are given there cost function and marginal cost function. And now we need to tell the total industry supply at the price of $6.

As we discussed in the earlier question above that firm chooses to produce as long as marginal cost is equal to price. Let's find out how much the firm would produce at a price of $6.

Marginal cost = 6

2y = 6

y = 6/2 = 3.

So a firm with a marginal cost function of 2y at a price of $6 will produce 3 units. Now note that there are 10 identical firms in the industry each one will be producing 3 units since each firm is identical. So to the total industry supply will be the sum of individual firm's supply.

Total industry supply = 3×10 = 30units

So the total industry supply will be 30 units at a price of $6.

The correct answer for this question is option C, 30.