When we have two alternatives to any action, i.e. there are two ways to arrive at a certain conclusion , or there are two choices to physically or ethically consume a product, that choice between the two options is referred to as the binary choice model.
There are various factors among the two binary choices that needs to be estimated to arrive at a conclusion or to finally choose any of the two choices, however, the most critical and the overall estimation that needs to be done is the ‘maximum likelihood’ of one of the options to be better than the other. We need to estimate which of the two choices has the maximum likelihood to achieve what we desire out of the two choices.
The linear choice model studies the relationship of quality between the outputs of the choices we have. The output with the best qualitative relationship is better preferred in the linear model of choices. The model in which only two options are possible for an outcome is referred to as the probit model of choice. For example, if we want to know the gender of an individual, there will be only two options, Male or Female.
Choices are very intrigue between various individuals. Economics shows the various ways in which we can make the appropriate choice between two different, mutually exclusive or coherent choices.
. Luxembourgers consume only coffee and cigarettes. Each Luxembourger has the same utility function u(x,y)-xay1-a, where...
3. A taxpayer has utility function U(x, L) = x ^1/2 − L where L is hours of labour supply and x is consumption. The taxpayer earns a wage of $4 per hour worked (which is fixed throughout the analysis). (a) Suppose that the government imposes a proportional (percentage) tax at rate τ on labour income, so that the taxpayer’s budget constraint is x = (1 − τ )4L. Solve for the optimal labour supply (L) and consumption (x) as...
Question 1: Colin's utility function for goods X and Y is represented by U(XY) = X0.5Y0.5 . Assume his income is $1000 and the prices of X and Y are $50 and S100, respectively. a. Write an expression for Colin's budget constraint. b. Calculate the optimal quantities of X and Y that Colin should choose, given his budget constraint. Graph your answer. Suppose that government subsidy program lowers the price of Y from $100 per unit to $ 50 per...
2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good X. Use the results from part (b) together with the ordinary demand function for good X to show that the Slutsky equation holds for this case. c) d) Prove that the expenditure function calculated in part (a) is homogeneous...
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of your budget on Chimichangas, which is totally reasonable after the Dumpling House tragedy. a) Solve the utility maximization problem, finding the uncompensated demand for x, & x, and the indirect utility function in terms of p,, p, and Y. b) Solve the expenditure minimization problem,...
8. Felix's preferences can be represented by the following utility function: u(x,k)-(p) s where x, and x2 denote the amounts consumed of goods 1 and 2, respectively. The prices of these goods are pi > 0 and p2 >0, respectively, and his wealth is w> 0. Thegovernment needs to collect a large amount of moneyto financea new Health Care plan, and contemplates two options: (i) Introduce an income tax equivalent to 40% offexswealth; or (ii) Chargea sales tax overthe price...
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180 to spend, and the price of X, PX = 4.50, and the price of Y, PY = 2 a. How much X and Y should the consumer purchase in order to maximize her utility? b. How much total utility does the consumer receive? c. Now suppose PX decreases to 2. What is the new bundle of X and Y that the consumer will demand?...
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and the consumer's income are unchanged....
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
3. Micheal has a utility function of the following: U(L, X) = Lº X1-a, where L is leisure and X is consumption. If he works, he receives real wage w. Outside of the labor market, he has non-labor market income V. And his endowment of time T is normalized to 1. And the price of goods p is also normalized to 1. (a) Please write down his budget constraint. (b) Assuming a = Į, V = 100, w = 200,...
Question 2 A consumer purchases two goods, food (x) and clothing (y). He has the utility function U(X,Y) = XY, where X and Y denote amounts of X and Y consumed. Marginal utilities of X and Y are MUx = y and MUy = x. The consumer’s income is $72 per week and that the price of y is Py = $1 per unit and price of x is Px1 = $9 per unit. What are his initial quantities of X and...