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A purely competitive firm finds that the market price for its product is $30. It has a fixed cost of $100 and a variable cost of $17.50 per unit for the first 50 units and then $37.50 per unit for all successive units. Instructions: Enter your answers rounded to two decimal places. a. Does price equal or exceed average variable cost for the first 50 units?            What is the average variable cost for the first 50 units?       $  per unit b. Does price equal or exceed average variable cost for the first 100 units?            What is the average variable cost for the first 100 units?       $  per unit c. What is the marginal cost per unit for the first 50 units?       $  per unit      The marginal cost for units 51 and higher?       $  per unit d. For each of the first 50 units, does MR exceed MC?            Is MR > MC for units 51 and higher?       e. What output level will yield the largest possible profit for this purely competitive firm?      units

Question

A purely competitive firm finds that the market price for its product is 30.Ithasafixedcostof30. It has a fixed cost of 100 and a variable cost of 17.50perunitforthefirst50unitsandthen17.50 per unit for the first 50 units and then 37.50 per unit for all successive units. Instructions: Enter your answers rounded to two decimal places. a. Does price equal or exceed average variable cost for the first 50 units?            What is the average variable cost for the first 50 units?        perunit b.Doespriceequalor exceedaveragevariablecostforthefirst100units?          Whatistheaveragevariablecostforthefirst100units?        per unit b. Does price equal or exceed average variable cost for the first 100 units?            What is the average variable cost for the first 100 units?        per unit c. What is the marginal cost per unit for the first 50 units?        perunit     Themarginalcostforunits51andhigher?        per unit      The marginal cost for units 51 and higher?        per unit d. For each of the first 50 units, does MR exceed MC?            Is MR > MC for units 51 and higher?       e. What output level will yield the largest possible profit for this purely competitive firm?      units

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Solution

a. Does price equal or exceed average variable cost for the first 50 units?

To determine this, we need to calculate the average variable cost (AVC) for the first 50 units.

Variable cost for the first 50 units = 17.50perunitTotalvariablecostforthefirst50units=50units17.50 per unit Total variable cost for the first 50 units = 50 units * 17.50/unit = $875

Average variable cost for the first 50 units = Total variable cost / Number of units Average variable cost for the first 50 units = 875/50=875 / 50 = 17.50 per unit

Since the market price is 30,whichisgreaterthantheAVCof30, which is greater than the AVC of 17.50, price exceeds average variable cost for the first 50 units.

What is the average variable cost for the first 50 units? $17.50 per unit

b. Does price equal or exceed average variable cost for the first 100 units?

To determine this, we need to calculate the average variable cost (AVC) for the first 100 units.

Variable cost for the first 50 units = 17.50perunitVariablecostforthenext50units(units51100)=17.50 per unit Variable cost for the next 50 units (units 51-100) = 37.50 per unit

Total variable cost for the first 100 units = (50 units * 17.50/unit)+(50units17.50/unit) + (50 units * 37.50/unit) Total variable cost for the first 100 units = 875+875 + 1875 = $2750

Average variable cost for the first 100 units = Total variable cost / Number of units Average variable cost for the first 100 units = 2750/100=2750 / 100 = 27.50 per unit

Since the market price is 30,whichisgreaterthantheAVCof30, which is greater than the AVC of 27.50, price exceeds average variable cost for the first 100 units.

What is the average variable cost for the first 100 units? $27.50 per unit

c. What is the marginal cost per unit for the first 50 units?

The marginal cost (MC) for the first 50 units is the same as the variable cost per unit for the first 50 units. Marginal cost per unit for the first 50 units = $17.50 per unit

The marginal cost for units 51 and higher?

The marginal cost (MC) for units 51 and higher is the same as the variable cost per unit for those units. Marginal cost for units 51 and higher = $37.50 per unit

d. For each of the first 50 units, does MR exceed MC?

Marginal revenue (MR) is equal to the market price, which is 30.Forthefirst50units,MR(30. For the first 50 units, MR (30) exceeds MC ($17.50).

Is MR > MC for units 51 and higher?

For units 51 and higher, MR (30)islessthanMC(30) is less than MC (37.50).

e. What output level will yield the largest possible profit for this purely competitive firm?

The firm should produce up to the point where MR equals MC. Since MR exceeds MC for the first 50 units but not for units 51 and higher, the firm should produce 50 units to maximize profit.

Output level that will yield the largest possible profit: 50 units

This problem has been solved

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