Heres an example of few of the 5 short tasks. 2. Suppose tha

Heres an example of few of the 5 short tasks. 2. Suppose that a consumer has utility given byU(x, y) =xy+10yand income of $100to spend on goods x and y.a. The prices ofxandyare both $1 per unit. Solve the problem to find the optimal basket of goods. b. Suppose that the price of x increases to $5 per unit. Solve the problem to find the new optimal basket of goods. Find the total effect of the price change on the consumption of each good. c. Calculate the substitution effect of the increase in the price of go od x on the consumption of each good. What income would the consumer need to attain the original level of utility when the price of x increases to $5 per unit? Find the income effect of the increase in the price of good x on the consumption of each good. Are the goods normal or inferior? Explain. e. Show that the total effect of the increase in the price of x is equal to the sum of the substitution effect and the income effect. firm has two variable factors and a production function f ( x 1 , x 2 ) = x 1 2 1 x 1 2 2 . The price of its output is 4, the price of factor 1 is w 1 , and the price of factor 2 is w 2 . a. Write the two equations that say that the value of the marginal product of each factor is equato to its wage. If w 1 = 2 w 2 , these two equations imply that x 1 x 2 = b. For this production function, is it possible to solve the two margi nal produc- tivity equations uniquely for x 1 and x 2 ?