Production function of William's Pizza Shop

Employees 0 1 2 3 4 5 6 7 8 The cost of an oven is 1,000,000,000,000,000,000,000,000,000,000,000, Employees are priced at 0 500 1000 1500 2000 2500 3000 3500 4000. Total price 1000 1500 2000 2500 3000 3500 4000 4500 5000 Pizza Count 0 75 180 360 600 900 1140 1260 1360 0 20.00 11.11 6.94 5.00 3.89 3.51 3.57 3.68 Average cost

In William's pizza shop's production function, which inputs are fixed and which are variable? What ranges appear to be rising, stable, or decreasing? and/or diminishing returns to the number of workers employed?

The fixed input in William's pizza shop is only the oven cost. The variable inputs are the labor cost per week and the quantity of pizza produced per week. From the table above the average cost decreases from workers 1 to 6 and then increases with 7and 8 workers.

What number of workers appears to be most efficient in terms of pizza product per worker?

Efficiency = Pizza Quantity ÷ Number of workers

Pizza Quantity 0 75 180 360 600 900 1140 1260 1360 Workers 0 1 2 3 4 5 6 7 8 Efficiency 0 75 90 120 150 180 190 180 170

6 workers are the most efficient since they are producing 190 pizzas in a week. This is the highest quantity of pizzas for any number of workers.

What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week?

Margin cost = Total cost ÷ quantity of Pizzas

Total cost = Fixed cost + variable costs

Total cost 1000 1500 2000 2500 3000 3500 4000 4500 5000 Pizza Quantity 0 75 180 360 600 900 1140 1260 1360 Average cost/ margin cost 0 20.00 11.11 6.94 5.00 3.89 3.51 3.57 3.68

The number of workers that appears to minimize the margin cost is 6 workers at a margin cost of $ 3.51 per pizza.

Why would marginal productivity decline when you hire more workers in the short run after a certain level?

Marginal productivity in the short run will decline when more workers are hired since the number of ovens is limited to only 4 ovens and therefore some workers will be idle. If more ovens are acquired marginal productivity will increase.

How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer.

Expanding the business will increase the production of pizzas; meanwhile, the fixed costs will remain constant. Therefore, this will lead to a reduction in fixed cost per unit of pizza produced up to a certain range. However, when fixed cost and production increases disproportionately diseconomies of scale will occur. As in the example, above diseconomies of scale occur when the 7th worker is hired. The average cost increased and the number of pizzas produced per worker decreased.

Q2.

Describe and derive an expression for the marginal cost (MC) curve.

Marginal cost equation is a derivative of the total cost equation.

TVC = TVC = 3450 + 20Q + 0.008Q2

MC = = 20 + 0.016Q

MC = 20 + 0.016Q

Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).

Cost of producing an extra unit is determined from the margin cost equation

MC = 20 + 0.016Q

Q = 200

MC = 20 + (0.016 X 200)

= $ 23.2

Adding the cost of leasing a new machine

Total additional cost = 2000 + 23.2

= $ 2023.2

What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.

At profit maximization marginal cost will be equal to the marginal revenue

MC = MR

Q = 4100 - 25P

Make P (price) the subject of the formula

P = (4100 - Q)/25

TR = P* Q

= Q* (4100-Q)/25

= 164Q- 0.04Q2

Marginal revenue is a derivative of total revenue, therefore,

MR=164-0.08Q

MR = MC

164Q- 0.08Q=20+0.016Q

0.096Q=144

Q=1500

P= (4100 - Q)/25

= (4100-1500)/25 = $ 104

Therefore, the profit maximizing quantity is 1500 pairs of shoes and the profit maximizing price is $ 104

d. Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week

In the short run the profit- maximizing quantity is 1500. Therefore, an expansion of 1200 will not lead to profit maximization. These mean that the cost of taking a lease of $ 2000 is not justifiable in the short run. In the long run, if there is demand, the company may consider taking the lease of $ 2000 for expansion but this is only justifiable if the demand is high.