The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: π = −10q + 2000[$] where q is the demand and π is the unit price for this product

a. Determine the maximum consumption of these consumers

b. Determine the price that no consumer is prepared to pay for this product

c. Determine the maximum consumers’ surplus. Explain why the consumers will not be able to realize this surplus

d. For a price π of 1000 $/unit, calculate the consumption, the consumers’ gross surplus, the revenue collected by the producers and the consumers’ net surplus.

e. If the price π increases by 20%, calculate the change in consumption and the change in the revenue collected by the producers.

f. What is the price elasticity of demand for this product and this group of consumers when the price π is 1000 $/unit

g. Derive an expression for the gross consumers’ surplus and the net consumers’ surplus as a function of the demand. Check these expressions using the results of part d

h. Derive an expression for the net consumers’ surplus and the gross consumers’ surplus as a function of the price. Check these expressions using the results of part d