All categories

3 years ago

Consider the following production function: Q=(L+K)1/2

Business

1 answer:

boyakko [2]3 years ago

8 0

Answer:

(a) MPL = 1/2

(b) MPK = 1/2

(d) APK = = L/2K+ 1/2

(e) TRSL,K = 1

Explanation:

Q = (L+K)1/2 = L/2 + K/2 ……………………………………………………. (1)

Where Q is the total output, L is Labour and K is capital

(a) What is the Marginal Product of Labor (MPL)?

To get MPL, differentiate equation (1) with respect to L as follows:

MPL = dQ/dL = 1/2

(b) What is the Marginal Product of Capital (MPK)?

To get MPK, differentiate equation with respect to K as follows:

MPK = dQ/dL = 1/2

Both MPL and MPK are diminishing since each of them is 1/2 which less than one.

(c) What is the Average Product of Labor (APL)?

To calculate APL, divide equation (1) by L as follows:

APL = Q/L = (L/2)/L + (K/2)/L

= 1/2+ K/2L

(d) What is the Average Product of Capital (MPK)?

To calculate APK, divide equation (1) by K as follows:

APL = Q/K = (L/2)/K + (K/2)/K

= L/2K+ 1/2

(e) What is the TRSL,K ?

TRSL,K implies Technical Rate of Subsitution of L for K = MPK/MPL

TRSL,K = MPK/MPL

Since both MPK and MPL are each equal to 1/2 as calculated under (a) and (b) above, we substitute for them in the TRSL,K as follows:

TRSL,K = MPK/MPL = (1/2)/(1/2) = 1

(e.1.) Is the absolute value of TRSL,K diminishing in L or K?

No, it neither diminishing in L nor K since the answer is equal to 1.

(e.2.) Are there constant, decreasing, or increasing returns to scale?

Since the TRSL,K is equal to 1, it implies there is a constant return to scale.

I wish you the best.

You might be interested in

Explain the theory of purchasing power parity (ppp). based on this theory, what is a general forecast of the values of currenci

Nadusha1986 [10]

Purchasing Power Parity or PPP deals with the fact that the purchasing power of a consumer should be similar either buying goods in a foreign country or in the home country. The exchange rate will adjust to maintain equal purchasing power if inflation in a foreign country differs from inflation in the home country.

7 0

2 years ago

Yolanda (41), a freelance photographer, reports a net profit of $50,000 on Schedule C, Profit or Loss from Business. This is her

AleksandrR [38]

Answer:

the self-employment tax is $7,065

Explanation:

The computation of the self-employment tax is given below:

Given that

net profit = $50,000

Now the 92.35% of net profit is $46,175

As it is lower than $128,400

So,

= 15.3% of $46,175

= $7,065

Hence, the self-employment tax is $7,065

6 0

2 years ago

A 30-year U.S. Treasury bond has a 4.0 percent interest rate. In contrast, a 10-year Treasury note has an interest rate of 2.5 p

iVinArrow [24]

Answer:

1.0 percent

Explanation:

Expected real rate of return can be described as the proportion of the annual return or profit from an investment after deducting inflation.

The purpose of the real rate of return is to show the accurate and actual purchasing power of a certain sum of money over a period of time.

An investor can therefore know what is the real return of a nominal return when the nominal interest is adjusted for inflation.

From the question, we have:

Interest rate on 10-year Treasury note = 2.5 percent

Expected Inflation = 1.5 percent

Therefore, the expected real rate of return on the 10-year Treasury note is derived by subtracting the 1.5 percent expected Inflation from the 2.5 percent interest rate on 10-year Treasury note as follows:

Expected real rate of return on the 10-year Treasury note = 2.5 - 1.5

= 1.0 percent

Therefore, the expected real rate of return on the 10-year U.S. Treasury note is 1.0 percent.

All the best.

4 0

3 years ago

Which of the following statements best defines the term credit according to the text?

polet [3.4K]

<span>B. A loan which is repaid with interest in monthly payments

</span>

5 0

3 years ago

Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.50 percent, a par value of $1,000 pe

katrin [286]

Answer:

2.9652%

Explanation:

to determine the cost of debt we must use the FMV of the bonds plus the YTM:

first bond:

FMV = 1.09 x $1,000 = $1,090 x 3,600 bonds = $3,924,000

YTM = {C + [(F - P)/n]} / [(F + P)/2] = {17.5 + [(1000 - 1090)/16]} / [(1000 + 1090)/2] = (17.5 - 5.625) / 1045 = 1.136% x 2 = 2.27% annual

second bond:

FMV = 0.95 x $2,000 = $1,900 x 3,950 bonds = $7,505,000

YTM = {C + [(F - P)/n]} / [(F + P)/2] = {59.4 + [(2000 - 1900)/42]} / [(2000 + 1900)/2] = (59.4 + 2.38) / 1950 = 3.168% x 2 = 6.34% annual

total debt = $3,924,000 + $7,505,000 = $11,429,000

weighted average after tax cost of debt:

{($3,924,000/$11,429,000 x 2.27%) + ($7,505,000/$11,429,000 x 6.34%)} x (1 - 0.40) = (0.779% + 4.163%) x 0.6 = 4.942% x 0.6 = 2.9652%

6 0

3 years ago