Cant figure out g and h The inverse demand function of a group of consumers for

Question

Cant figure out g and h

The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: --I0q+ 2000[S] where q is the demand and 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 For a price 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 increases by 20%, calculate the change in consumption and f. What is the price elasticity of demand for this product and this group of g. Derive an expression for the gross consumers' surplus and the net consumers' the change in the revenue collected by the producers, consumers when the price is 1000 $/unit 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

Explanation / Answer

Consider the give4n problem here the demand curve is given by, “P = 2000 – 10*Q”.

So, here the “gross consumer surplus” is the area under the demand curve and the “net consumer surplus” is given by the area under the demand curve and above the price level.

So, the above demand function can be written as, “Q = 200-P/10”.

So, the gross consumer surplus is given by.

=> integration(2,000-10*Q)dQ = 2,000*Q-10*Q^2/2 = 2,000*Q-5*Q^2.

Now, the “net consumer surplus” is given by.

=> 2,000*Q-5*Q^2 – P*Q = 2,000*Q-5*Q^2 – (2,000-10*Q)*Q = 2,000*Q-5*Q^2 – 2,000*Q+10*Q^2 = 5*Q^2.

So, if “P=1000”, => the corresponding quantity demanded is given by, “Q=(2000-1000)/10=100.

So, the gross and net consumer surplus are given by.

=> 2000*Q-5*Q^2 = 2000*100-5*100^2 = 150,000.

Now, “5*Q^2 = 5*100^2 = 50,000.

h).

Now, the above demand function can also be written as, “Q=200-P/10”.

So, the “gross consumer surplus” is given by, “2,000*Q-5*Q^2”.

=> 2,000*(200-P/10) – 5*(200-P/10)^2.

Similarly, the “net consumer surplus” is given by.

=> 5*Q^2 = 5*(200-P/10)^2.

So, if “P=1000”, => the gross consumer surplus is given by, “2,000*(200-P/10)-5*(200-P/10)^2”, “2,000*(100)-5*(100)^2 = 150,000”.

Similarly, the “net consumer surplus” is given by, “5*(200-P/10)^2 = 5*100^2 = 50,000.

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