Question

At a workers utility maximizing level of leisure and income, their marginal utility with

respect to leisure is 5, their marginal utility with respect to income is X, their hourly

wage is $6, and their non-labor income is $50. What must X

equal?

A. 5/56

B. 5/6

C. 30

D. 6

3. Suppose the price of labor increases. In the long run, the amount of capital a firm uses

A. will increase

B. will decrease

C. may increase or decrease

D. will remain unchanged

4. Suppose we are studying the labor market for Italian restaurants. Which of the following

scenarios will

not

shift the labor supply curve.

A. Competing restaurants are willing to pay chefs/cooks higher salaries

B. The price of the machine to make pasta dough increases

C. A new law provides sick-days to workers in the food industry

D. None of the above

Answer #1

**At a workers utility maximising level of leisure and
income, their marginal utility with respect to leisure I.e
MU _{l}= 5 and marginal utility with respect to income is x
, I.e MUc = X.
Now wage rate is $6 I.e w= $6 and their non- labor income is
$50,**

**Now the utility maximising condition will
be:**

**Marginal rate of substitution between labor and leisure
i.e MU _{l}/ MUc = wage rate (w)**

**Hence, 5/X = 6**

**or, 6X = 5 or, X= 5/6.
Hence the answer will be: B. 5/6.**

**3. We know that the optimal input mix condition for a
firm is:**

**MP _{l}/ MP_{k} = w/r**

**where, MP _{l} = Marginal product of labor and
MP_{k}= Marginal product of capital, w= price of labor and
r= price of capital.**

Now in the long run when the price of labor increases, w/r increases and MP_{l}/MP_{k} < w/r.

Hence for MP_{l}/ MP_{k} to increase, MP_{k} should fall which means level of capital should increase. Also if MP_{l}/ MP_{k} remains unchanged, w/ r should fall which means that wage rate should fall and then firms will substitute capital with labor and the amount of capital will fall. Hence the answer will be:

**C. May increase or
decrease.**

**4. The following scenario will not shift the labor supply
curve:**

**B. The price of the machine to make pasta dough
increases**

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