Hello, please help with the following questions (25-29). The first image is there for reference

a Andreoni-Miller preferences and a Dictator Game Consider a dictator game in which the price of giving differs from 1, as in the Andreoni and Miller experiment. Specifically, let x, represent the amount of an endowment of 30 that the dictator keeps, x, the amount that the recipient receives as a result of the dictator's gift, and suppose the price of giving is 0.5. Thus, the budget constraint is: x, +0.5.x, = 30 In addition, suppose throughout this section that the dictator has Andreoni-Miller (i.e., CES) preferences, and consider the following cases of different parameter values for the dictator's utility function Case 1: p= 0 25. Write the dictator's utility function, u,, for this case. 26. Write the equation that represents the relationship between x, and x, at the optimum. That is, for this dictator, write an equation with x, on the left and x, on the right. 27. Solve for the optimal value of x, x. Hint: use the budget constraint and the result from the previous problem. 28. Solve for the optimal value of x, X;. Check that x, and x, satisfy the budget constraint. 29. What is the value of the dictators utility, U,, at this optimum? a Andreoni-Miller preferences and a Dictator Game Consider a dictator game in which the price of giving differs from 1, as in the Andreoni and Miller experiment. Specifically, let x, represent the amount of an endowment of 30 that the dictator keeps, x, the amount that the recipient receives as a result of the dictator's gift, and suppose the price of giving is 0.5. Thus, the budget constraint is: x, +0.5.x, = 30 In addition, suppose throughout this section that the dictator has Andreoni-Miller (i.e., CES) preferences, and consider the following cases of different parameter values for the dictator's utility function Case 1: p= 0 25. Write the dictator's utility function, u,, for this case. 26. Write the equation that represents the relationship between x, and x, at the optimum. That is, for this dictator, write an equation with x, on the left and x, on the right. 27. Solve for the optimal value of x, x. Hint: use the budget constraint and the result from the previous problem. 28. Solve for the optimal value of x, X;. Check that x, and x, satisfy the budget constraint. 29. What is the value of the dictators utility, U,, at this optimum