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Please make sure your answer is correct! Please refer carefully to the hints Q8 (d)Here are some hints. (i). According to the hint, directly solve y through x=(M-Py^)/(2Px) and xPx+yPy=M (i.e., Budget constraint/ budget line) 8. Emma consumes only two goods, x and y . Initially, price of x is P x = $1 . Price of y is P y = $1 . Her income is $30 . (a) Draw the budget line in a (x,y)-space. Clearly indicate the intercept values. Draw indifference curves to illustrate Emma's consumption choices in x and y . [Numerical values for x and y are not needed and not known in this question.] (b) If both prices of x and y increase by 10% (to $1.1 ), draw the new budget lines with new intercept values indicated. Then, draw indifference curves to illustrate Emma's consumption choices in x and y [Numerical values for x and y are not needed and not known in this question.] (c) Suppose that, after the price-increase in (b), Emma's income also increases by 10% . Illustrate Emma's new consumption choices after this change, and compare the new choices with the choices in (a). (d) An economist estimates Emma's demand function of x to be x = ( M P y a ) / ( 2 P x ) , where M is Emma's income. (i) What is the demand function of y? [Hint: use the budget constraint.] (ii) What is the value of ? [Hints: Use the answers from (c). Also, you may or may not need the mathematical rule, ( x y ) k = x k y k and ( 1 ) k = 1 . This is for your reference only] [Note: Part (d) of this question is difficult. Students should be able to do (a) to (c). For part (d), try your best.] .

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Please make sure your answer is correct! Please refer carefully to the hints Q8 (d)Here are some hints. (i). According to the hint, directly solve y through x=(M-Py^)/(2Px) and xPx+yPy=M (i.e., Budget constraint/ budget line) 8. Emma consumes only two goods, x and y . Initially, price of x is P x = $1 . Price of y is P y = $1 . Her income is $30 . (a) Draw the budget line in a (x,y)-space. Clearly indicate the intercept values. Draw indifference curves to illustrate Emma's consumption choices in x and y . [Numerical values for x and y are not needed and not known in this question.] (b) If both prices of x and y increase by 10% (to $1.1 ), draw the new budget lines with new intercept values indicated. Then, draw indifference curves to illustrate Emma's consumption choices in x and y [Numerical values for x and y are not needed and not known in this question.] (c) Suppose that, after the price-increase in (b), Emma's income also increases by 10% . Illustrate Emma's new consumption choices after this change, and compare the new choices with the choices in (a). (d) An economist estimates Emma's demand function of x to be x = ( M P y a ) / ( 2 P x ) , where M is Emma's income. (i) What is the demand function of y? [Hint: use the budget constraint.] (ii) What is the value of ? [Hints: Use the answers from (c). Also, you may or may not need the mathematical rule, ( x y ) k = x k y k and ( 1 ) k = 1 . This is for your reference only] [Note: Part (d) of this question is difficult. Students should be able to do (a) to (c). For part (d), try your best.] .

- 1. Please make sure your answer is correct! Please refer carefully to the hints Q8 (d)Here are some hints. (i). According to the hint, directly solve y through x=(M-Py^)/(2Px) and xPx+yPy=M (i.e., Budget constraint/ budget line) 8. Emma consumes only two goods, x and y . Initially, price of x is P x = $1 . Price of y is P y = $1 . Her income is $30 . (a) Draw the budget line in a (x,y)-space. Clearly indicate the intercept values. Draw indifference curves to illustrate Emma's consumption choices in x and y . [Numerical values for x and y are not needed and not known in this question.] (b) If both prices of x and y increase by 10% (to $1.1 ), draw the new budget lines with new intercept values indicated. Then, draw indifference curves to illustrate Emma's consumption choices in x and y [Numerical values for x and y are not needed and not known in this question.] (c) Suppose that, after the price-increase in (b), Emma's income also increases by 10% . Illustrate Emma's new consumption choices after this change, and compare the new choices with the choices in (a). (d) An economist estimates Emma's demand function of x to be x = ( M P y a ) / ( 2 P x ) , where M is Emma's income. (i) What is the demand function of y? [Hint: use the budget constraint.] (ii) What is the value of ? [Hints: Use the answers from (c). Also, you may or may not need the mathematical rule, ( x y ) k = x k y k and ( 1 ) k = 1 . This is for your reference only] [Note: Part (d) of this question is difficult. Students should be able to do (a) to (c). For part (d), try your best.]