demo, MySQL - rextester

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#MySQL 5.7.12
#please drop objects you've created at the end of the script 
#or check for their existance before creating
#'\\' is a delimiter

DROP TABLE IF EXISTS pricelist_merchant;
CREATE TABLE pricelist_merchant (Merchant varchar(55), product_id int, price decimal(10,2), qty int);
INSERT INTO pricelist_merchant (Merchant, product_id, price, qty)
VALUES
    ('Merch_A', 3217, 44.30,  16),
    ('Merch_Z', 3217, 45.14,  2),
    ('Merch_U', 3217, 45.62,  16),
    ('Merch_I', 3217, 46.06,  16),
    ('Merch_Q', 3217, 48.98,  55),
    ('Merch_B', 3217, 39.58,  0),
    ('Merch_T', 3217, 45.97,  0),
    ('Merch_M', 3217, 46.40,  0),
    ('Merch_L', 3220, 105.84, 1),
    ('Merch_Z', 3220, 147.00, 3),
    ('Merch_U', 3220, 149.36, 2),
    ('Merch_A', 3220, 149.99, 2),
    ('Merch_Q', 3220, 153.53, 90),
    ('Merch_I', 3220, 154.51, 2),
    ('Merch_T', 3220, 157.41, 4),
    ('Merch_C', 3220, 164.59, 46),
    ('Merch_M', 3220, 136.10, 0),
    ('Merch_B', 3220, 136.71, 0);

SELECT t1.*
FROM pricelist_merchant t1
INNER JOIN
(
    SELECT
        product_id,
        MIN(CASE WHEN qty > 0 THEN price END) AS min_price_qty,
        MIN(CASE WHEN qty = 0 THEN price END) AS min_price_no_qty
    FROM pricelist_merchant
    WHERE product_id <> '0'
    GROUP BY product_id
) t2
    ON t1.product_id = t2.product_id AND
       t1.price      = COALESCE(t2.min_price_qty, t2.min_price_no_qty)
ORDER BY t1.product_id;


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