Problem 6. An economist has estimated the demand equation of a certain product as Q=100-2.5P where P is the price unit and Q is the quantity demanded (in thousands) per year.

a.Calculate and interpret the own price elasticity of demand of the product when its price goes from $10 to $15 per unit.

b. Calculate the own price elasticity when price is P=30. Is demand elastic, unit-elastic or inelastic at price P-$30? Will you raise or lower price to increase revenue?

c. Determine the total consumer value when price is P=$30.

d. Suppose the inverse demand function for a monopolist's product is given by P-230-1.5Q and the total cost function is TC=500+300+3.50Q^2 so that its marginal cost is MC=30+7Q

e. Determine the marginal revenue (MR) as a function of Q.

f. Determine the profit-maximizing price and quantity.

g. Determine the maximum profits.