Suppose that when neither input exceeds four times the other, capital and labor are perfect substitutes at a one-to-one ratio. However, once the input ratio reaches four to one in favor of either input, no further substitution is possible. Draw the isoquants.

When the production function is linear, q = 0.20L + 0.10K, the factors are perfect substitutes for one another and the isoquant is linear. Determine the equation for the isoquant when output equals 200 units. K= Assuming capital is plotted on the vertical axis and labor is plotted on the horizointal axis, what is the marginal rate of technical substitution (MRTS) in this case? MRTS = - (Enter a numeric response using a real number rounded to two decimal places.) tv MacBook Air DII F4 F6 F7 FB F10 F3 %23 & 3 4 5 7 8 { [ E R Y P D F G H J K > C N M command option .. .. - B >

Suppose a production function is given by the equation Q = LVK. 1. Graph the isoquants corresponding to Q = 10, and Q = 20. 2. MP = √K and MP = 0.5(L/VK). Find the Marginal Rate of Technical Substitution LK (MRTSLK). Do these isoquants exhibit diminishing marginal rates of technical substitution? (Does the slope get flatter as L increases?) 3. The cost of labor is w = $5 per labor hour and the cost of capital is r = $15 per machine hour. What is the equation of the $1500 iso-cost curve?

For each of the following cases, determine whether the firm should (A) Use more labor and less capital, or (B) Use more capital and less labor. 1. The marginal rate of technical substitution is 2 (i.e., the marginal product of labor is twice the marginal product of capital) and the input price ratio is 3 (i.e., a unit of labor costs three times as much as a unit of capital) 2. The marginal rate of technical substitution is 2 (i.e., the marginal product of labor is twice the marginal product of capital) and the input price ratio is 1 (i.e., a unit of labor costs the same as a unit of capital) 3. The marginal rate of technical substitution is initially equal to the input price ratio, but the firm's machines depreciate, so that the marginal product of capital decreases. 4. The marginal rate of technical substitution is initially equal to the input price ratio, but the firm successfully negotiates a lower rate of rent for their machines, so that the price of capital decreases. 5. The…