Suppose a consumer had a utility function given by: U= 2X + 5Y. If the price of Good X (Px) is $6 and the price of Good Y is $2 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $12? (Round to the nearest two decimal places if necessary.)

suppose the utility function of Vivian is U=602/3Y1/3. The unit priice of Good X is $10 while the unit price of Good Y is $30. Vivian has a budget of $1,800 to be spent on Good X and Good Y.  Find the optimal consumption bundle of vivian show your calculations.

Mary has the following utility function: u(x, y) = 3 ln(x) + 2y. Her income is given by I = 10 and the prices originally are p = 1 and py = 2 (b) How much of each good is Mary currently consuming?

A consumer has utility (see image) on ice creams (x) and cakes (y).   (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x).  (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.

For the utility function U = (Qx0.5+Qy0.5)² and the budget 122 = 8Qx + 8Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).

3) The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y) ?

Suppose a consumer had a utility function given by: U=X + 4Y. If the price of Good X (Px) is $1 and the price of Good Y is $8 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $4? (Round to the nearest two decimal places if necessary.)