Microeconomic questions

Question 1: Cost function, Conditional Input Demand [25 points} Being driven by the high profit from digital asset trading, Doggycoin, Sulfiltar has decided to set-up his own digital mining company. Let's assume that two main essential inputs in digital asset production be the higthuality graphic card [Cl and electricity {E}. After observing the business for few months, he finds the production function as Cobb-Douglas technology as the following: 9125. E) = are Where :3 is continuous, strictly increasing, and strictly quasi-concave and q[) = I]. Answer the following questions: a. If the prices of graphic card and electricity denoted by c and a, respectively, and we assume the cost-minimizing behavior. Solve for C and E in their prices and output level, and what is the total cost function He, .5, q]? [15 p15} b. What are the conditional demands for input C and E? on pts]