Answer to Question #194168 in Microeconomics for fahmida

Question

11. Patty’s Pizza has the production function per hour shown in the table below. The hourly wage rate for  each worker is $10. Each pizza sells for $2. 

Quantity of workers - 0, 1, 2, 3, 4, 5.

Quantity of pizza - 0, 9, 15, 19, 22, 24.

Now, let’s assume that Patty buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9, and so on.  

e) Calculate the new MPL and the new VMPL at the original price of $2 per pizza using the new information above.  f) Using answer (e) determine how Patty’s hiring decision responds to this increase in the productivity of her workforce when the wage rate is $10, i.e., will she hire more workers or less workers than before or not change the number of workers? (use a diagram)

Answer 1

(e) Table showing the old and new MP_L and VMP_L is given below.

VMP_{L =} 2 × MP_L

(f) Equilibrium condition for choosing the number of workers is

VMP_L = w

If VMP_L exceeds the wage rate, it is optimum to hire more workers because the output generated by an additional unit of labour is more than what the firm has to pay to hire him. Similarly if VMP_L is less than the wage rate, it is profitable for the firm to reduce the number of workers.

Going by this logic, with the original productivity of the workers and with a wage rate of $10, Patty should hire 2 workers. This is because if she hires 3 workers, then wage becomes more than the VMP_L.

Now if productivity doubles, and with the same wage rate as before, she should hire 4 workers.

In the above diagram number of labourers is measured on the horizontal axis and wage rate is measured on the vertical axis. The yellow line represents the wage rate. We see that due to the improvement in labour productivity, VMP_L curve has shifted to the right from VMPL1 to VMPL2. Number of workers hired has increased from 2 to 4.