Question

QUESTION 11
(Calculation Problem)
Suppose a for-profit nursing home can produce long-term care services (x) using two inputs: labor (such as nurses, l) and material (such as drugs, M). Thus, the production function of the nursing home can be described as x = f(l, M). In addition, w represents the market price of labor input (wage) and p represents the market price of material inputs. Thus, the cost function of the nursing home can be described by C = w × l + p × M. Answer the following questions:
a. Use a graph to explain how the nursing home decides the optimal uses of labor and material inputs. (2 pts)
b. Suppose the government imposes a regulation on minimum nursing staffing and this minimum nursing staffing level exceeds the level the nursing home decides is optimal for itself. Use a graph to explain the effect of government regulation on the nursing home’s input choices for the following two conditions. Does regulation affect the cost of nursing home care if the nursing home wants to keep its output constant? What other choices can the nursing home make if the nursing home wants to keep costs constant in response to government regulation? (2 pts, 2 pts)
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Answer 1

Prodution function: x = f(l,m)

Cost function: C = w*l + p*m

w = wage

p = market price of material input

A.

The intersection of labor demand and labor supply in a competitive market, gives the wage rate of labor and optimal level of Labor (l) to hire.

With the same amount of labor and intersection with production function, provides the material input (M). Thus the nursing home should operate at L labor units and M units of material.

B. Let min. no of nursing staff = L*. Also L* > l(the optimal level).

If output stays constant,

As the labor increases from l to l*, we see excess supply in the economy and with which to keep the output constant, production function flattens from F(l,m) to F(l*,m).

With excess supply in the market, conditioned in output remaining constant,

1.If there is an increase in demand which leads to dd curve moving upwards and meeting the supply curve at l* labor level, will lead to the increase in wage rate. As seen by the green lines.

If wages are to be kept constant,

The demand and supply should increase to to reach the same level wage rate (W). As shown by blue lines.