Exam 7: Production Cost: Many Variable Inputs

A producer has a production function given by: y(l₁,l₂)= l₁^0.5+2l₂^0.5 where y is the level of output and l₁ and l₂ are two different types of labour that are employed. Their cost is w₁ and w₂ respectively. a)Suppose that the input prices are both equal to w and that the output sells at price p. What is the optimal employment of two types of labour as a function of p and w? b)Suppose that p=10, w=5. What is the optimal quantity of output produced? What is the corresponding profit? c)What returns to scale does the production function exhibit?

An isoquant may be defined as a curve showing all combinations of inputs:

Which of the following is an example of increasing returns to scale?

What is the marginal rate of technical substitution for the production function y = (1200z₁z₂)^1/2 when Z₂=200 and z₁=100?

The output- expansion path connects the cost- minimizing input- bundles that:

The first principle of cost minimization is:

An isoquant curve is the set of input bundles such that:

The production function f(z₁,z₂)= min(z₁,z₂)exhibits:

For any homothetic production function:

One reason why supply curves slope upward to the right is because:

The LRMC curves will have a downward sloping portion if:

An isoquant represents combinations of:

Long run and short run total cost functions are:

Suppose Tariq's body shop operates with the production function y = (300z₁z₂)^1/2. If w1=20 and w2=60, what is the minimum cost of producing 3000 units?

Natural Farms Ltd. produces yogurt using milk and bacteria culture in fixed proportions. It takes one pint of milk and one ounce of bacteria culture to make a pint of yogurt. The price of milk is $0.50 per pint, and bacteria culture costs $0.10 an ounce. i)Draw one or two isoquants for Natural Farms Ltd. ii)How much does it cost to produce one pint of yogurt? Two pints? Three pints? iii)What is Natural Farms' cost function?

What the cheapest input bundle for producing 60 units if f(L,K)= min(3L,2K)?