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For each of the following, sketch a curve with the appropriate shape given the assumptions:

(a) An Engel curve for x, where preferences for x and y take a Cobb-Douglas form.

(b) An Income Consumption Curve (ICC), if both x and y are normal at lower levels of income, whilst at higher income levels, y is inferior.

(c) A Price Consumption Curve (PCC) for y, where the demand for y is perfectly price-inelastic.

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