Suppose the firm's production function is Q = K1/3L2/3, where the MPK = 
and MPL = 
.
a. If the rental rate of capital R = $30 and the wage rate W = $40, what is the cost-minimizing capital-to-labor ratio?
b. If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?
Definitions:
Probability
The measure of the likelihood that an event will occur, often expressed as a number between 0 and 1, where 1 indicates certainty.
Premium
A premium refers to the additional amount paid for a product, service, or insurance policy over and above its basic cost.
Risk Reduction
Strategies or actions taken to decrease or mitigate the level of risk.
Expected Value
A statistical measure that calculates the average outcome of a random variable or process, factoring in all possible values and their probabilities.
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