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A firm has a production function of the form Y=2L+5K where Y is the output and L and K are the two inputs. The unit cost of L is $2 and per unit cost of K is $3.

Draw an iso-cost line for this firm, showing combinations of L and K that cost $6 and another iso-cost line showing combinations that cost $12. What are the slopes of these iso-cost lines? Sketch the production isoquant depicting 10 units of output. Find the minimum cost of producing 10 units of output.

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Related questions

Ben and Geri have changed their production methods and are now producing ice cream according to the production function,

Y=KL,

1. The price of a machine is R= 2 dollars and a laborer costs W= 1 dollar, the expenditure level E=$8, Determine the slope of the iso-expenditure curve

2. By setting the MRTS equal to the slope of the iso-expenditure curve, determine the mascot-minimizing capital-labor ratio (K/L) with R=2 and W=1. Given that the firm wants to produce Y=8 units of output, what is the optimal level of capita and labor for the firm? what is the cost-minimizing level of expenditure E when the firm produces Y=8 pints of ice cream?

3.Suppose the price of a laborer goes up to W=2. What are the new cost-minimizing levels of capital and labor given that Ben and Geri are still producing Y=8 pints of ice cream? What is the new cost-minimizing level of expenditure

Consider a bus company that has the following production function: T(L,K) = L, where T is the number of passengers served by the company (i.e., output), L is labor, and K is capital. Assume that the unit price for L is 1 and that for K is 4. The company is required to serve T passengers.
a. Write down the cost-minimization problem for the bus company.
b. Derive the slope of the isoquant curve, i.e., derive MRTSL,K and the slope of iso-cost curve.
c. Derive the optimality condition (tangency condition), which shows the relationship between L and K at the cost-minimizing point.
d. Substitute the optimality condition into the production function, and express cost-minimizing L a function of T. Is L * increasing with T? In the same way, express cost-minimizing K as a function of T. Substitute these functions (L * and K * ) into the cost expression C =wL + rK Express the minimized cost as a function of T, i.e., derive the cost function. Illustrates the relationship between Cand T by drawing a curve. Determine whether the firm’s cost function exhibits IRTS or DRTS and briefly explain.

constant costs

increasing returns to scale

constant returns to scale

isocost curve

decreasing returns to scale

isoquant

diseconomies of scale

long-run average cost

economies of scale

long-run marginal cost

economies of scope

marginal rate of technical substitution

expansion path

short-run expansion path

___A curve that displays all the various combinations of inputs that will produce a given amount of output.

___The rate at which one input is substituted for another along an isoquant.

___Line that shows all the possible combinations of inputs that can be purchased for a given total cost.

___A curve showing all of the cost-minimizing levels of input usage for various levels of output.

___When the usage of all inputs is increased by an equal proportionate amount, output ___increases by exactly the same proportion.

___When the usage of all inputs is increased by an equal proportionate amount, output increases by a larger proportionate amount.

___When the usage of all inputs is increased by an equal proportionate amount, output increases by a smaller proportionate amount.

___Cost per unit in the long run.

___The change in long-run total cost per unit change in output.

___When long-run average cost falls as output increases.

___When long-run average cost increases with increases in output.

___Long-run average and marginal costs are equal for all levels of output.

___The situation in which the joint cost of producing two goods is less than the sum of the separate costs of producing the two goods.

___Horizontal line showing the cost-minimizing input combinations for various output levels when capital is fixed in the short run.

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