Question

Please i need help with this question,2nd time of posting,please no spam of u related answers,

Thanks.

4· P.T. Barnum is concerned about the health of his star trapeze artist. If the artist is capable of performing a triple somersault, PT's revenues will be m2. If however his star crashes and is unable to perform, revenues will only be mi. Lloyds of London is willing to offer PT insurance on the following terms the premium for every dollar of insurance to be paid in the event of an accident-is γ·PT's expected utility function is EU (c1: ca)-T1 In (cı ) + π21n (ca), where cı is his consumption in the event of an accident; his consumption if his trapeze star performs the triple somersault, T1 the probability of an accident, and T2 the probability of suc- cessfully completing the somersault (a) If r is the number of dollars of accident insurance purchased, derive equations which indicate the amount of consumption if there is an ac cident and if there is not an accident. Use these equations to determine the budget constraint between ci and c2. What is the price of an extra dollar of C1 in terms of C2? Why? (b) Determine PT's demand functions for ci and o2 (c) If the probability of an accident is 5%, γ = .05, m1 = 100, and m2 = 5000, what are ci and c? Is PT fully insured? On a diagram draw PT's budget constraint, his best indifference curve, and his optimal bundle (d) How much better off is PT for the ability to buy insurance? Show this on an expected utility diagram.

Answer 1

The given data is * P. T Bamum is connected about the heath of his star frapere exist rightarrow P T's revenues with be = m_2 rightarrow Revenues will only be = m_1 rightarrow PT's expected utility function is E U (c_1, c_2) = pi_1 ln (c_1) + pi_2 ln (c_2) (a) If x is the number of dollars of accident insurance purchased total amount of premium to be paid is y x consumption if there is an accident c_2 = M_2 - y_x + x c_2 = M_2 + x (1 - y) - (i) rightarrow consumption is there is no accident c_1 = m_1 - y x - (ii) from the equation (i) and (ii), then we get the \r\n c_2 - m_2/1 - y = m_c - c_1/y y_c_2 - y_m_2 = (1 - y) m_1 - (1 - y) c_1