Question

Please I need today answer for This question and it is very important and I need solution for this issue with all the details , and help me with all the details.Please write your answer to me by typing, not by handwriting, so that I can read and understand your answer clearly.BR/Hassa

Q) Assume that the demand for going to hospitals is given by p=10-2q and the society’s marginal cost curve is given by p=2q. The individuals are insured and do not have to pay anything for the visits. Derive and show the number of visits to hospitals by the individuals and the welfare loss in a figure. Explain.

Answer 1

The demand curve p = 10-2q represents the private marginal benefit (PMB) as well as social marginal benefit (SMB) curve in this case since there is no positive external benefit. The intercept of the curve is 10 and slope = -2. Hence, the demand curve touches the price axis at 10 and quantity (hospital visit axis at 5.

On the other hand, the private marginal cost (PMC) = 0 (i.e., the individuals do not need to pay). Hence, the private marginal cost curve overlaps with horizontal axis. In other words, the horizontal axis represents the market supply curve. We also have social marginal cost (SMC) curve as p = 2q, which is shown in the figure as a positively sloped straight line passing through origin and slope = 2.

The number of visits is determined at the intersection of the private marginal benefit curve and private marginal cost curve. Since private marginal cost = 0, the solution is arrived when p = 10-2q = 0, i.e.., q = 5. Therefore, the number of visits will be 5 (point D) in the figure. With 5 visits, the welfare loss will be the area of the triangle ESD = (1/2) * SD * EX. We know that DS = 10 (since social marginal cost = 2*5 =10). To find the length of EX = X₁D , we may first find OX₁. When PMB = SMC, 10-2q = 2q => 4q = 10 => q = 2.5. Hence, OX₁=X₁D=EX = 2.5. Therefore, welfare loss = (1/2)*(2.5)*10 = 12.5

Price/Cost 2 X 3 Hospital visit