1. Denote the number of children by n and the survival probability of a child to adult- hood by . A parental household derives utility out of consumption (c), the number of surviving offspring (n) and child expenditures (h). Preferences are specified as follows = uln(cc) B₁ ln(n · π(ñ, h)) + ẞ2 In(h), ẞ1 > B2, (1) where the parameter c> 0 reflects subsistence consumption. Child survival is given by π = π + (1 − µñ)λh, ≥ 0, x > 0. (2) is exogenous to the household and positively affected by average income y such (y). The representative household's budget constraint reads as that y = c + nhy (3) a) Solve the household's utility maximisation problem. b) Show and explain how fertility n responds to changes in households' income y. c) Show and explain how n and h respond to changes in 7. 2. Assume now that all households are identical such that y = y. a) In light of your results obtained in 1., show that the reaction of population growth in response to a change in income can be expressed as dgL dy C 1 = Nπ - Ly(y μπ π 1 - TT / მყ . (4) Hint: Population growth gr is determined by the number of surviving children. The populations growth rate is therefore nл. The total differential delivers the above equation. b) In light of (4), explain how the model can generate a hump-shaped correlation between income y and population growth (No derivations! Just provide an economic rationale based on your findings).

View image and please calculate for first funciton.

1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…

If a person lives for 3 years with a disease and the current standard of care for that disease means he/she lives with a utility level of 0.7.-What is the QALY?   Answer in not less than 300 words

for b) and c) can you derive an equation to show the changes caused by the change in parameters

Can you do questions 1a 2a and 2b can you send solutions through pictures as it will be easy to follow.

PLEASE SHOW SOLUTIONS AND PLEASE DO THIS TYPEWRITTEN FOR UPVOTE

6. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmic

If the utility function (U) between food (F) and clothing (C) can be represented as U = F*C, then which combination of food and clothing will a rational consumer choose? a. (F, C) = (9, 25) O b. (F, C) = (25, 4) O c. (F, C) = (4, 16) d. (F, C) = (4, 25)

V*(p1, p2, 1) = True False P₁ P₂ 1² is a valid indirect utility function.