Question

A pineapple pizza place is making pizza with a cost function c(y) =10+(y²)/2+3y where y is the number of pizza made .

a) Suppose the restaurant decides to make 10 pizzas, the average variable cost of making 10 pizza is: $_______

b) The marginal cost of the 10th pizza is: $_______

c) If the restaurant decides to make an additional pizza, the average variable cost will:

		Increase
		Decrease
		Stay the same
		Not enough information to determine

Answer 1

Given, Total cost = TC = c(y) = 10 + (y²)/2 + 3y

(a) Total variable costs (TVC) are those costs which depend on the level of output. Average variable costs (AVC) are total variable cost per unit of output. Thus,

AVC = TVC/Q

Here, TVC = (y²)/2 + 3y

and AVC = TVC/y = [(y²)/2 + 3y] / y = (y/2) + 3

At y= 10 pizzas,

AVC = (y/2) + 3 = (10/2) + 3 = 5 + 3 = 8

Thus,  the average variable cost of making 10 pizza is: $8.

(b) Marginal cost (MC) is given by the change in total cost upon change in output.

MC = ∆TC / ∆Q = TC_n - TC_n-1

Here, MC = ∆TC / ∆y = dTC/dy = d[10 + (y²)/2 + 3y]/dy = y + 3

MC at y = 10,

MC = 10 + 3 = 13

Alternatively,

TC of 9 pizzas =  10 + (y²)/2 + 3y = 10 + (9²)/2 + 3*9 = $77.5

TC of 10 pizzas = 10 + (y²)/2 + 3y = 10 + (10²)/2 + 3*10 = $90

MC of 10th pizza = TC of 10 pizzas - TC of 9 pizzas = $90 - $77.5 = $12.5

Thus, The marginal cost of the 10th pizza is: $12.5~$13.

(c) The AVC of the 11 pizzas will be

AVC' = (y/2) + 3 = (11/2) + 3 = 8.5

The change in AVC is given by

AVC' - AVC = 8.5 - 8 = $0.5

Alternatively,

Slope of AVC = dAVC/dy = 1/2 = 0.5 (positive slope)

Since the change in AVC is positive, so the average variable costs will increase by $0.5 if the restaurant decides to make an additional pizza.

Thus, the answer is increase.