Consider the following CES function 0-1 0-1 = A( aK, + (1 – a)L,º As o → 0, prove the Leontief production function Y; = A min(K+, L;).

The function Q = L0.3 + K0.7  is an example of _____ returns to scale of production.

Provethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scale

Show that the two-input Cobb-Douglas production function (attached) has decreasing return in scale (DRS), constant return of scale (CRS) or increasing return of scale (ITS) depending on if alpha1 + alpha2 is smaller than, equal, or larger than 1.

The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = c₂LC1C²2 C2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co 5, C₁ = 0.25, and c2₂ 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. = = where co, C₁, and Max s.t. L, C ≥ 0 A ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L ≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when…