Business

EconomicsQ&A LibraryA perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (a) Prove that this production function has decreasing returns to scale. (b) Find the optimal (cost-minimizing) ratio of capital to labor inputs K L for any level of output (use scale expansion path). (c) For any q, nd the cost minimizing inputs as functions of output: i.e., derive functions L(q) and K(q).Question

Asked Dec 11, 2019

2 views

A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (a) Prove that this production function has decreasing returns to scale. (b) Find the optimal (cost-minimizing) ratio of capital to labor inputs K L for any level of output (use scale expansion path). (c) For any q, nd the cost minimizing inputs as functions of output: i.e., derive functions L(q) and K(q).

Step 1

Following information is given:

Step 2

**a)** For analyzing of it has decreasing returns to scale,

Step 3

Since, **f(K , L) > f(aK , aL)**, the function has decreasing returns to scale. This means that, if more of input is added, the output will decrease.

**b)** for findi...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Suppose a company is considering buying a new copier. The new machine is less labor intensive, and w...

A: a) Since the company is considering to buy a new copier which is less labor intensive than and will ...

Q: he following problem traces the relationship between firm decisions, market supply, and market equ...

A: The following table gives us the various cost production of different unit of outputs.We are given w...

Q: Name 10 countries with the highest policy rate and the impact of the policy rate on their economies

A: The countries having the highest policy rates as of 2019 are listed in the table

Q: 4) Suppose the economy is in a long-run equilibrium a)Draw the economy’s short-run and long-run Phil...

A: The Phillips curve shows the inverse relationship between inflation and unemployment in the economy....

Q: Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) ...

A: The production function for widgets is given by:

Q: The Third National Bank has reserves of $20,000 and checkable deposits of $100,000. The reserve rati...

A: It is given that the required reserve ratio (rr) is 10% or 0.10.Monetary multiplier (M) is the degre...

Q: Suppose the price level reflects the number of dollars needed to buy a basket of goods containing on...

A: Suppose, the in year one the price of the basket is $7.00 and $6.00 in year two. We can find the cha...

Q: According to Marx, surplus value is the source of profit. Discuss how surplus value is maximized in ...

A: Surplus value in simple words means value added. Labor is used by the capitalist in producing their ...

Q: What are the consequences for including a proxy for an omitted variable?

A: The bias in the OLS estimator can be caused due to the omitted factor or based on the variable facto...