A short run equilibriam production function is given as Q= X¹
⁰, where X is the amount of capital and labor used in production.
If the price of capital is $2 and the price of labor is $1, what is the optimal combination of capital and labor to maximize output?
The optimal combination of capital and labor to maximize output is X = 5. This is because the marginal product of capital (MPC) is 10X⁹ and the marginal product of labor (MPL) is 10X. Setting the MPC equal to the price of capital ($2) and the MPL equal to the price of labor ($1) yields the equation 10X⁹ = 2 and 10X = 1. Solving for X yields X = 5.